If you suspect the center of the universe probably exists, would you share your definition of it? For instance, the center of a line segment is the point equidistant from its endpoints.
Wouldn't that point then be the center of expansion? As I understand things, galaxies are not moving through space as pieces from an explosion would move through the air. Rather, the space between galaxies is itself expanding. But I'm not a physicist, astronomer, or cosmologist, and there are plenty of them around here to straighten it out.
I think most confusion about the balloon analogy results from it being a 2D model of a 3D concept. People forget or don't realize this and think the center of the 3D balloon would be the center of the universe or other such extrapolations.